Question
Find Least Common Multiple of 209, 43, 89 and 75 using prime factorisation method.
Answer
LCM( 209, 43, 89, 75 ) = 59988225
Explanation
Step 1: Write down factorisation of each number:
209 = 11 · 19
43 = 43
89 = 89
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
| 209 | = | 11 | · | 19 | ||||||||||
| 43 | = | 43 | ||||||||||||
| 89 | = | 89 | ||||||||||||
| 75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 209 | = | 11 | · | 19 | ||||||||||||
| 43 | = | 43 | ||||||||||||||
| 89 | = | 89 | ||||||||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||
| LCM | = | 3 | · | 5 | · | 5 | · | 11 | · | 19 | · | 43 | · | 89 | = | 59988225 |
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